Particles collide with first object then die on second collision
Yes, it's possible: collisions are defined per-object, not per-particle system, so you can define as many types of collisions as you want.

Just enable the "Collisions" physics on both objects, checking the "kill particles" box only for the second one.



If the second object comes from a water/ocean simulation, make sure that the "collision" modifier is the last one on the modifier stack.



(for clarity, in my example I've checked "Render dead particles")